Specific Weight to Vertex Group
Invert your selection and assign that to the vertex group. By nature, vertexes with zero weight are either in the vertex group for a weird reason, or not in it at all. You cannot say “be not in this group with a weight of one.” The vertex group you’re creating should be for the “pins” AKA the still parts of the trampoline, rather than to assign the cloth. It is set up this way since the cloth simulation will of course assume everything is cloth. The vertex group is telling it what isn’t.